Question: Simplify the following expression: $ q = -6 - \dfrac{-7x - 7}{4x + 9} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4x + 9}{4x + 9}$ $ \dfrac{-6}{1} \times \dfrac{4x + 9}{4x + 9} = \dfrac{-24x - 54}{4x + 9} $ Therefore $ q = \dfrac{-24x - 54}{4x + 9} - \dfrac{-7x - 7}{4x + 9} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-24x - 54 - (-7x - 7) }{4x + 9} $ Distribute the negative sign: $q = \dfrac{-24x - 54 + 7x + 7}{4x + 9}$ $q = \dfrac{-17x - 47}{4x + 9}$